Hostilities are persisting in the main rebel-held city of Donetsk, as well as around the towns of Debaltseve and Schastye.
Donetsk airport, the focus of much of the fighting, has no immediate tactical significance for separatist forces devoid of any air power.
However, the government's hold on the facility gives it a strategic position to attack rebel positions in the city.
At least 3,660 people have been killed over six months of fighting, according to UN estimates. The UN says some deaths reported since the September 5 truce agreement may include individuals killed before that date.
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UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein said in a statement that the security crisis needed to be tackled so residents of east Ukraine could reclaim their rights to education, adequate health care, housing and employment.
The UN estimates some 5 million people are being deprived of their basic rights in east Ukraine.
"While the cease-fire is a very welcome step toward ending the fighting in eastern Ukraine, I call on all parties to genuinely respect and uphold it, and to halt the attacks on civilians and civilian infrastructure," Zeid said.
Separatist fighters have been observed firing artillery from residential areas, eliciting hasty responses from Ukrainian troops that often miss their mark and hit houses.
The UN report cites the Ukrainian government as saying more than 4,500 residential buildings have been damaged or destroyed in the fighting. At least 22 settlements remain without running water, while another 93 settlements have no electricity, the report said.
Lack of proper housing is becoming particularly acute with the approach of winter, when temperatures in the region can drop below freezing for weeks on end.